jmc

Fill in grid lines to make the shape look like a small 6x6 checkerboard. There are $6\times 6=36$ squares total. The smallest shaded region has $3$ squares. The medium shaded region has $7$ squares. The largest shaded region has $11$ squares. The total shaded area is $3+7+11=21$ squares. Thus, $\frac{21}{36}=\frac{7}{12}$ of the square is shaded, and the answer is $\boxed{\frac{7}{12}}$